My boss asked me, he's heard it from me and now his brother-in-law and he tried googling it and of course sees all the "fact check" stuff that no, mRNA doesn't change your dna.
There are a lot of Mikovitz and Tenpenny videos out there but he'd probably be more receptive to something in print.
They (the MSM etc) are actually saying that mRNA doesn't change your DNA.
The mRNA vaccines (Pfizer/Moderna) have almost zero capacity to write to DNA. There is machinery to write RNA to DNA but that machinery is not present in the vaccines (if it is what it says it is). The adenovirus vaccines (J&J/AZ) have a higher chance, because the adenovirus injects actual DNA into the nucleus, but even here such an occurrence would be very rare.
Even if one of these vaccine contents was written to DNA the most likely scenario is that the cell would be killed by the immune system since that's the purpose of the vaccines.
There is no fear of genetic modification in any meaningful way from the vaccines from a biological standpoint, unless again, the vaccines have ingredients other than what they say they do, and I have seen no evidence to support that idea.